{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:XNROPHHU54YD5HZCSG2GN2MAP3","short_pith_number":"pith:XNROPHHU","canonical_record":{"source":{"id":"2605.28786","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-27T17:46:28Z","cross_cats_sorted":[],"title_canon_sha256":"043a64d934f593ec50ac49bd9a5182dc6caa16d3f4f39a6a8ab9420fd4d31c34","abstract_canon_sha256":"8054de52afbbd2d7909942c6e46daf172d00b6088bdd9aae8db1f02a9ae44d43"},"schema_version":"1.0"},"canonical_sha256":"bb62e79cf4ef303e9f2291b466e9807ee69a33f24583433a2e5246d7145430e1","source":{"kind":"arxiv","id":"2605.28786","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.28786","created_at":"2026-05-28T02:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2605.28786v1","created_at":"2026-05-28T02:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28786","created_at":"2026-05-28T02:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"XNROPHHU54YD","created_at":"2026-05-28T02:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"XNROPHHU54YD5HZC","created_at":"2026-05-28T02:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"XNROPHHU","created_at":"2026-05-28T02:05:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:XNROPHHU54YD5HZCSG2GN2MAP3","target":"record","payload":{"canonical_record":{"source":{"id":"2605.28786","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-27T17:46:28Z","cross_cats_sorted":[],"title_canon_sha256":"043a64d934f593ec50ac49bd9a5182dc6caa16d3f4f39a6a8ab9420fd4d31c34","abstract_canon_sha256":"8054de52afbbd2d7909942c6e46daf172d00b6088bdd9aae8db1f02a9ae44d43"},"schema_version":"1.0"},"canonical_sha256":"bb62e79cf4ef303e9f2291b466e9807ee69a33f24583433a2e5246d7145430e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:05:03.581140Z","signature_b64":"NDSrKKeiOcPDTlgejKFNpxwCgTnYBpFAHjF2ZRSKuzisrPHP0OCsNSLwAZGzfOTX98uXGuUCXXMf8mA0ryEWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb62e79cf4ef303e9f2291b466e9807ee69a33f24583433a2e5246d7145430e1","last_reissued_at":"2026-05-28T02:05:03.580743Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:05:03.580743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.28786","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-28T02:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eeq/A6baXTghVZ38nlRKr+5dchV04HFKVFAt1gyhrV+ZBD2lQpMztYPs2jzgmM4LFLZr5xFiG56LyhgZRZ2DCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:54:49.766242Z"},"content_sha256":"d8f32884251de1f73e6f50ab0df991ae566e983fc4eb75c8bb179629f8f367da","schema_version":"1.0","event_id":"sha256:d8f32884251de1f73e6f50ab0df991ae566e983fc4eb75c8bb179629f8f367da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:XNROPHHU54YD5HZCSG2GN2MAP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A quantum harmonic analysis approach to nonlinear time-frequency concentration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Erling Svela, S. Ivan Trapasso","submitted_at":"2026-05-27T17:46:28Z","abstract_excerpt":"We study nonlinear concentration problems for time-frequency distributions in the Cohen class. Using recent techniques from quantum harmonic analysis (QHA) we provide both positive and negative results, such as sufficient conditions for the existence of optimizers in terms of the ``window operator'' and explicit examples where the supremum is never attained. We also study the structural properties of window operators, in particular operators that yield weakly continuous concentration functionals and operators for which the nonlinear concentration problem admits an optimizer. We then consider g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28786","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.28786/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-28T02:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nrxjrex13+YGKY+QyW+3o6VskmFTggIOW/692PfcI6+ZThUEJTzNXz1rTsSqAQRc8nnXYzUghe1qe4dhtVt+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:54:49.766832Z"},"content_sha256":"3ca82fdc92858dcf8820fbb28c464ddbff6ea903268cc582a86f3cbd37beece6","schema_version":"1.0","event_id":"sha256:3ca82fdc92858dcf8820fbb28c464ddbff6ea903268cc582a86f3cbd37beece6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNROPHHU54YD5HZCSG2GN2MAP3/bundle.json","state_url":"https://pith.science/pith/XNROPHHU54YD5HZCSG2GN2MAP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNROPHHU54YD5HZCSG2GN2MAP3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T16:54:49Z","links":{"resolver":"https://pith.science/pith/XNROPHHU54YD5HZCSG2GN2MAP3","bundle":"https://pith.science/pith/XNROPHHU54YD5HZCSG2GN2MAP3/bundle.json","state":"https://pith.science/pith/XNROPHHU54YD5HZCSG2GN2MAP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNROPHHU54YD5HZCSG2GN2MAP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XNROPHHU54YD5HZCSG2GN2MAP3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8054de52afbbd2d7909942c6e46daf172d00b6088bdd9aae8db1f02a9ae44d43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-27T17:46:28Z","title_canon_sha256":"043a64d934f593ec50ac49bd9a5182dc6caa16d3f4f39a6a8ab9420fd4d31c34"},"schema_version":"1.0","source":{"id":"2605.28786","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.28786","created_at":"2026-05-28T02:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2605.28786v1","created_at":"2026-05-28T02:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28786","created_at":"2026-05-28T02:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"XNROPHHU54YD","created_at":"2026-05-28T02:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"XNROPHHU54YD5HZC","created_at":"2026-05-28T02:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"XNROPHHU","created_at":"2026-05-28T02:05:03Z"}],"graph_snapshots":[{"event_id":"sha256:3ca82fdc92858dcf8820fbb28c464ddbff6ea903268cc582a86f3cbd37beece6","target":"graph","created_at":"2026-05-28T02:05:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.28786/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study nonlinear concentration problems for time-frequency distributions in the Cohen class. Using recent techniques from quantum harmonic analysis (QHA) we provide both positive and negative results, such as sufficient conditions for the existence of optimizers in terms of the ``window operator'' and explicit examples where the supremum is never attained. We also study the structural properties of window operators, in particular operators that yield weakly continuous concentration functionals and operators for which the nonlinear concentration problem admits an optimizer. We then consider g","authors_text":"Erling Svela, S. Ivan Trapasso","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-27T17:46:28Z","title":"A quantum harmonic analysis approach to nonlinear time-frequency concentration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28786","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d8f32884251de1f73e6f50ab0df991ae566e983fc4eb75c8bb179629f8f367da","target":"record","created_at":"2026-05-28T02:05:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8054de52afbbd2d7909942c6e46daf172d00b6088bdd9aae8db1f02a9ae44d43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-27T17:46:28Z","title_canon_sha256":"043a64d934f593ec50ac49bd9a5182dc6caa16d3f4f39a6a8ab9420fd4d31c34"},"schema_version":"1.0","source":{"id":"2605.28786","kind":"arxiv","version":1}},"canonical_sha256":"bb62e79cf4ef303e9f2291b466e9807ee69a33f24583433a2e5246d7145430e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb62e79cf4ef303e9f2291b466e9807ee69a33f24583433a2e5246d7145430e1","first_computed_at":"2026-05-28T02:05:03.580743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T02:05:03.580743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NDSrKKeiOcPDTlgejKFNpxwCgTnYBpFAHjF2ZRSKuzisrPHP0OCsNSLwAZGzfOTX98uXGuUCXXMf8mA0ryEWDg==","signature_status":"signed_v1","signed_at":"2026-05-28T02:05:03.581140Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.28786","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8f32884251de1f73e6f50ab0df991ae566e983fc4eb75c8bb179629f8f367da","sha256:3ca82fdc92858dcf8820fbb28c464ddbff6ea903268cc582a86f3cbd37beece6"],"state_sha256":"5502386f7bc0066b8f08300ad31ad2ec8eeb900501331f75d1b4eeae42724b26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nkpqZqSow7+HZ4PPjc/u0i27gyeInBjFcTo97b2rjZuMozf+usGIlFKvl4ShVh1yLWSNjtiHnkOMOrQwDYzEAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:54:49.770504Z","bundle_sha256":"a2df14139e91be4a65f54ef98f1030bab82af3325f97109d27c170cef4ba0c87"}}